Articulating vertebrae with asymmetrical and variable radius of curvature

ABSTRACT

An endoscope has a first segment with a proximal end and a distal end and is symmetric about an axis. A second segment, comprising a flexible and interconnected linkage system, is pivotably coupled to the first segment and, when subject to an applied force, is configurable along an arc having a variable radius of curvature. The linkage system is capable of articulation through an angle from zero degrees through about 280 degrees.

PRIOR APPLICATION

[0001] Applicant claims priority benefits under 35 U.S.C. §119(e) of U.S. Provisional Patent Application Serial No. 60/384,775 filed May 30, 2002 which is incorporated herein by reference thereto as if set forth at length.

FIELD OF THE INVENTION

[0002] The present invention relates to an endoscope shaft and, more particularly an endoscope shaft made of articulating vertebrae that when subject to a force, are configurable along an arc having a variable radius of curvature.

BACKGROUND OF THE INVENTION

[0003] Conventional endoscopes can be articulated in different directions; however, typically these endoscopes cannot be articulated with a variable radius of curvature nor to an angle of more than 180 degrees. Often the endoscope has only a single radius of curvature for the entire articulating length of the shaft. Further, the conventional endoscopes that use articulating vertebrae use a number of vertebrae with identical dimensions connected in series and all oriented the same way.

[0004] By limiting the endoscopes to a single radius of curvature, the user of the endoscope is limited as to the regions of the body that are readily accessible by articulation of the endoscope. Because of the limited ability to articulate the endoscope, there is a need for an articulating endoscope capable of being articulated with varying degrees of curvature to permit the operator to locate the endoscope in various locations within the body. Such an endoscope requires a shaft capable of being manipulated with more than one radius of curvature.

SUMMARY OF THE INVENTION

[0005] An endoscope has a first segment with a proximal end and a distal end and is symmetric about an axis. A second segment, comprising a flexible and interconnected linkage system, is pivotably coupled to the first segment and, when subject to an applied force, is configurable along an arc having a variable radius of curvature. The linkage system is capable of articulation through an angle from zero degrees through about 280 degrees.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006]FIG. 1 is a side view of an endoscope shaft with articulating vertebrae.

[0007]FIG. 2 is a side view of an endoscope shaft in FIG. 1 showing the vertebrae articulated in two different directions.

[0008]FIG. 3 is an enlarged view of a segment of the articulated vertebrae shown in FIG. 2.

[0009]FIG. 4 is a top sectional view of a single vertebra.

[0010]FIG. 5 is a side view of the vertebra shown in FIG. 4.

[0011]FIG. 6 is an end view of the vertebra shown in FIG. 4.

[0012]FIG. 7 is another side view of the vertebra shown in FIG. 4.

[0013]FIG. 8 is a sectional end view of the vertebra shown in FIG. 7.

[0014]FIG. 9 is a top sectional view of a second vertebra.

[0015]FIG. 10 is a side view of the vertebra shown in FIG. 9.

[0016]FIG. 11 is an end view of the vertebra shown in FIG. 9.

[0017]FIG. 12 is another side view of the vertebra shown in FIG. 9.

[0018]FIG. 13 is a sectional end view of the vertebra shown in FIG. 12.

[0019]FIG. 14 is a side view of the vertebrae as seen in FIGS. 5, 7, 10 and 12 showing guide wires.

[0020]FIG. 15 is a top sectional view of the vertebrae as seen in FIGS. 4 and 9 showing guide wires.

[0021]FIG. 16 is a sectional view of the vertebrae of FIG. 14.

[0022]FIG. 17 is a side view of an endoscope shaft with articulating vertebrae showing guide wires.

[0023]FIG. 18 is a side view of a segment of an endoscope shaft with articulating vertebrae showing moments developed therein due to forces applied to guide wires.

[0024]FIG. 19 is a sectional view of the segment of the endoscope of FIG. 18 showing guide wire symmetry.

[0025]FIG. 20 is a sectional view of the segment of the endoscope of FIG. 18 showing asymmetrical guide wires.

[0026]FIG. 21 is a sectional view of the segment of the endoscope of FIG. 18 showing asymmetrical guide wires.

[0027]FIG. 22 is a side view of a segment of an endoscope shaft with articulating vertebrae showing dimensions by which the radius of curvature of the endoscope is calculated.

[0028]FIG. 23 is a first view showing a configuration of the vertebrae of FIG. 3 articulated along an arc of decreasing radius on the surface of a cone.

[0029]FIG. 24 is a second view showing a configuration of the vertebrae of FIG. 3 articulated along an arc of increasing radius on the surface of a cone.

[0030]FIG. 25 is a view of the endoscope of FIG. 3 accessing remote and out of the way regions of a kidney.

DETAILED DESCRIPTION OF THE INVENTION

[0031] Referring first to FIG. 1, an articulating endoscope shaft 100 is shown at rest or in an unarticulated configuration along an axis 106. The articulating endoscope shaft 100 has a first insertion shaft segment 102. A second, flexible shaft segment 108 is a linkage system comprising a first set of articulating links or vertebrae 110 attached to and extending over a distance L₁ from a distal end 116 of the first insertion shaft segment 102. A third, flexible shaft segment 112 comprising a second set of articulating links or vertebrae 114 is attached to and extends over a distance L₂ from the second shaft segment 108. The first insertion shaft segment 102 is connected, at a proximal end 104 thereof, to an endoscope handpiece 164. A distal end 118 of the endoscope 100 and the articulating vertebrae 110, 114 are manipulated by way of the endoscope handpiece 164 through the use of control wires (not shown in FIG. 1) that are threaded through the endoscope 100 and attached to the vertebrae 110, 114.

[0032]FIG. 2 shows the endoscope shaft 100 articulated in two different directions or configurations θ₁ and θ₂. Articulated in a first direction θ₂, the vertebrae 110, 114 can be manipulated in such a manner that the vertebrae 110, 114 are displaced from the axis 106 along a first arc 122 wherein the vertebrae 120 (FIG. 3) furthest from the distal end 116 of the first insertion shaft segment 102 is rotated through an angle θ₂ in the range from zero degrees to about 280 degrees. In a similar fashion, when articulated in a second direction θ₁, the endoscope shaft 100 can be manipulated in such a manner that only the vertebrae 114 are displaced form the axis 106 along a second arc 124 wherein the vertebrae 120 furthest from the distal end 116 of the first insertion shaft segment 102 is rotated through an angle θ₁ in the range from zero degrees to about 180 degrees. FIG. 2 shows the endoscope shaft 100 articulated through an angle of θ₁ equal to about 180 degrees, in a direction opposite of the direction shown in FIG. 3, where only the smaller vertebrae 114 are articulated and the articulated endoscope shaft 100 has only one radius of curvature R₁.

[0033]FIG. 3 shows an enlarged view of the articulating vertebrae segment 108, 112 of the endoscope shaft 100 rotated along an arc 106 a having a variable radius of curvature. FIG. 3 shows the endoscope shaft 100 articulated through an angle of about 280 degrees using two different sizes of vertebrae 110, 114. The articulating segment of the endoscope shaft 100 is made up of two segments 108, 112. The first segment 108 uses relatively large diameter (D₁) vertebrae 110 with longer lengths L₃ or L₄ and the second segment 112 uses relatively smaller diameter (D₂) vertebrae 114 with smaller lengths L₅ or L₆. The use of different diameter vertebrae 110, 114 results in the articulating segment of the endoscope shaft 100 capable of having a different angle of manipulation (e.g., θ₁ or θ₂) and a different radius of curvature (e.g., R₁ or R₂) for different articulating segments of the endoscope shaft 100. FIG. 3 shows the first articulating segment 108 of the endoscope shaft 100 with the larger vertebrae 110 having a larger radius of curvature, R₂, than the second articulating segment 112 of the endoscope shaft 100 which has a smaller radius of curvature R₁. The larger vertebrae 110 can be seen in detail in FIGS. 4-8, while the smaller vertebrae 114 can be seen in detail in FIGS. 9-13.

[0034] FIGS. 4-8 show several views of an articulating vertebrae 110. The articulating vertebrae 110 is generally cylindrical in nature and symmetric about the axis 106 with an outside diameter D₁ (FIG. 8). The articulating vertebrae 110 includes a front face 126, 128 and a rear face 130, 132. The front face 126, 128 may be beveled at an angle of θ₃ or θ₄ where θ₃ and θ₄ range from zero degrees to about thirty degrees. As best understood from FIG. 5, θ₃ may equal θ₄ or θ₃ may be different from θ₄. Furthermore, the rear face 130, 132 may be beveled at an angle of θ₅ or θ₆ where θ₅ and θ₆ range from zero degrees to about thirty degrees. As best understood from FIG. 5, θ₅ may equal θ₆ or θ₅ may be different from θ₆. Yet further, the articulating vertebrae 110 includes a first pivot member 134 projecting from the front face 126, 128 and a second pivot member 136 projecting from the rear face 130, 132. The front face 126, 128 includes an aperture 142 therein having a rotational axis 144 coincident with the axis 106. As best understood from FIGS. 4 and 5, a pair of the second pivot members 136, of width W₁ apart (FIG. 6), on one articulating vertebrae 110, fit securely within a pair of the first pivot members 134 such that any two adjacent and linked pair of articulating vertebrae 110 pivot about a pivot axis 144 to the extent permissible by the front and rear beveled faces 126, 128, 130, 132. The articulating vertebrae 110 is also characterized by either a length, L₃ (FIG. 5) or length L₄ (FIG. 7) which spans the distance between successive pivot points 144 in the linkage system 108.

[0035] FIGS. 9-13 show several views of an articulating vertebrae 114. The articulating vertebrae 114 is generally cylindrical in nature and symmetric about the axis 106 with an outside diameter D₂ (FIG. 13). The articulating vertebrae 114 includes a front face 146, 148 and a rear face 150, 152. The front face 146, 148 may be beveled at an angle of θ₇ or θ₈ where θ₇ and θ₈ range from zero degrees to about thirty degrees. As best understood from FIG. 10, θ₇ may equal θ₈ or θ₇ may be different from θ₈. Furthermore, the rear face 150, 152 may be beveled at an angle of θ₉ or θ₁₀ where θ₉ and θ₁₀ range from zero degrees to about thirty degrees. As best understood from FIG. 10, θ₉ may equal θ₁₀ or θ₉ may be different from θ₁₀. Yet further, the articulating vertebrae 114 includes a first pivot member 154 projecting from the front face 146, 148 and a second pivot member 156 projecting from the rear face 150, 152. The front face 146, 148 includes an aperture 162 therein having a rotational axis 144 coincident with the axis 106. As best understood from FIGS. 9 and 10, a pair of the second pivot members 156, of width W₂ apart (FIG. 11), on one articulating vertebrae 114 fit securely within a pair of the first pivot members 154 such that any two adjacent and linked pair of articulating vertebrae 114 pivot about the pivot axis 144 to the extent permissible by the front and rear beveled faces 146, 148, 150, 152. The articulating vertebrae 114 is also characterized by either a length, L₅ (FIG. 10) or length L₆ (FIG. 12) which spans the distance between successive pivot points 144 in the linkage system 112.

[0036] By combining articulated segments 108, 112 having different diameters, bevel angles, lengths and numbers of vertebrae 110, 114, the articulating endoscopic shaft 100 can be manipulated to have two or more radii of curvature (e.g. R₁, R₂) when articulated in a single direction as seen in FIG. 3, depending upon which articulated segment of the endoscopic shaft 100 is manipulated or actuated. By using vertebrae 110, 114 having different diameters, D₁, D₂, where D₁ is greater than D₂, a greater torque, T, (or moment) may be developed in the corresponding vertebrae 110, 114 for D₁ than for D₂ due to the application of a force by the wire guides 166 (FIGS. 14-16) and as such allowing the vertebrae 110, 114 to be configurable along an arc having a variable radius of curvature. As best understood D₂ may be greater than or equal to D₁. An explanation of the moments developed in the endoscope will be explained in regard to FIGS. 18-21. Also, the positions of the vertebrae 110, 114 can be arranged in any combination of diameters, bevel angles, lengths, moment arms and numbers of vertebrae 110, 114, along the articulating endoscopic shaft 100 so as to have asymmetrical ranges of manipulation (e.g., θ₁≠θ₂) or variable radii of curvature (e.g., R₁≠R₂). Such combination of diameters, bevel angles, lengths, moment arms and numbers of vertebrae may be such that the asymmetrical ranges of manipulation or variable radii of curvature are effected depending upon in which direction the endoscopic shaft 100 is manipulated with respect to the axis 106. If the endoscopic shaft 100 is articulated in one direction with respect to the axis 106, it could have a larger angle or range of manipulation and/or radius of curvature, while if it is articulated in the opposite or a different direction with respect to the axis 106, it could have a smaller angle or range of manipulation and/or smaller radius of curvature. Furthermore, the same segment of the articulating endoscopic shaft 100 could have a different radius of curvature or angle of manipulation, depending upon the direction the shaft is articulated.

[0037] The arrangement of the vertebrae 110, 114 can also permit the endoscopic shaft 100 to be bent or manipulated in a single direction with respect to the axis 106 with different radii of curvature for different segments of the shaft 100. By adjusting the lengths, L₃, L₄, of different vertebrae 110, 114 or the number of each vertebrae 110, 114 used in each section 108, 112 of the articulating segment of the shaft 100, the endoscopic shaft 100 can be designed to have any number of combinations of radii curvatures for manipulation. For example, the endoscopic shaft 100 can be designed to have an increasing or decreasing radius of curvature as articulation of the articulated segments 108, 112 increases or decreases. The vertebrae 110, 114 and endoscopic shaft 100 can be specifically designed with the various radii of curvature needed to access specific areas within a body. By adjusting the number, length, diameter and bevel angle of the face of the vertebrae 110, 114, one can affect the bending properties of the articulated endoscopic shaft 100, such as symmetry with respect to the axis 106, the angle of articulation (e.g., θ₁, θ₂) and radius of curvature (e.g., R₁, R₂).

[0038] The vertebrae 110, 114 can be joined in any number of ways. FIG. 3 shows a series of large diameter vertebrae 110 pivotably connected to a series of smaller diameter vertebrae 114. The larger diameter vertebrae 110 are pivotally connected in series by mating and connecting the pivot members which extend from each end of each vertebrae 110, 114. The smaller diameter links 114 are pivotally connected in a similar manner. The ends of each of the vertebrae 110, 114 has a beveled surface which makes contact with the end surface of each adjacent vertebrae 110, 114 when the endoscopic shaft 100 is articulated. The larger the bevel angle, the greater the potential angle of articulation of the shaft because, as each vertebrae 110, 114 is actuated, it will continue to move in a particular direction until it comes in contact with its adjacent vertebrae and can no longer be actuated. By using vertebrae of different length and different bevel angles, one can control the bending properties of the endoscopic shaft 100.

[0039] Each vertebrae 110, 114 has two openings or slots 138, 140, 158, 160 in its side that define means for guiding the guide wires 166 that are manipulated to articulate the first and second segments 108, 112 of the shaft 100. The vertebrae 110, 114 can be oriented in a variety of ways with respect to the openings 138, 140, 158, 160 in their sides. For example, the vertebrae 110, 114 could be assembled in a manner where the orientation of the openings 138, 140, 158, 160 for each consecutive vertebrae 110, 114, is rotated through an angle θ₁₁ with respect to an adjacent vertebrae (e.g. 180 degrees). As such, a first guide wire 166 passing through the inside of the vertebrae 110, on one side of the endoscopic shaft 100, would therefore be attached to every other vertebrae 110 that had its openings 138, 140 oriented on the same side of the endoscopic shaft 100. A second guide wire 166 passing through the opposite side of the endoscopic shaft 100 would be attached to all the other vertebrae 114 that were oriented to have their openings 158, 160 on the opposite side of the endoscopic shaft 100. As seen in FIG. 17, the guide wires 166 are woven through the side openings 138, 140, 158, 160 in each or every other vertebrae 110, 114. The guide wires 166 are attached only to the end vertebrae 120. FIG. 16 shows that the guide wires 166 may be offset at an angle of θ₁₁. It will also be understood that the angle θ₁₁ may vary from one vertebrae to the next.

[0040]FIG. 18 depicts a side view of a segment of the endoscope shaft 100 with articulating vertebrae 110, 114, showing moments, M₁, M₂ developed about the rotational axis 144 due to forces F_(c1) and F_(c2) applied to guide wires 166. The forces are applied at distances d₁ and d₂ (moment arms) from the axis 106 and the moment M_(i)=F_(ci)×d_(i), i=1,2. Three conditions are possible in the arrangement of the guide wires 166 whereby different moments are developed. FIG. 19 depicts a sectional view of the segment of the endoscope shaft of FIG. 18 showing guide wire symmetry whereby d₁=d₂ and M₁=M₂ for equal forces F_(c1) and F_(c2). FIG. 20 depicts a sectional view of the segment of the endoscope shaft of FIG. 18 showing asymmetrical guide wires whereby d₁<d₂ and M₁<M₂ for equal forces F_(c1) and F_(c2). FIG. 21 depicts a sectional view of the segment of the endoscope shaft of FIG. 18 showing asymmetrical guide wires whereby d₁>d₂ and M₁>M₂ for equal forces F_(c1) and F_(c2). The asymmetrical guide wire conditions of FIGS. 20 and 21 may also be effected as in FIG. 19 by adjusting d₁ and d₂ therein. The asymmetrical guide wire condition allows the endoscope shaft 100 to be articulated through an angle θ₂ of from zero degrees through about 280 degrees.

[0041]FIG. 22 is a side view of a segment of an endoscope shaft with articulating vertebrae 110, 114 showing the dimensions V_(L), Ω, by which the radius of curvature, R₁, R₂, of the endoscope can be calculated. The radii of curvature, R₁, R₂ can be calculated from the Equation (1): $\begin{matrix} {R_{i} = \frac{V_{L}}{2\quad {\sin \left( \frac{\sum\Omega}{2{\sum V}} \right)}}} & (1) \end{matrix}$

[0042] where i=1, 2. In Eq. 1 V_(L) is the length of the vertebrae, Ω is the bend angle between adjacent vertebrae, ΣΩ is the total bend angle, ΣV is the total number of vertebrae links.

[0043] As seen in FIGS. 23 and 24 and as best understood from FIGS. 2, 3, 16 and 19-21, due to the angular location of the guide wires 166 about the axis 106, or the angular rotation of a front face of a vertebrae with respect to a rear face thereof (i.e. the value of θ₁₁), and the varying moments developed in the first and second segments 108, 112 of the endoscope, the arc 106 a along which the first and second segments 108, 112 are configured may lie either within a plane or on the surface of a geometrical body such as a cone 174 such that the arc 106 a is extraplanar in nature. Such out of plane configuration, as well as an angle of articulation of greater than 180 degrees, of the endoscope 100 allows, for example, a surgeon much greater flexibility in viewing or accessing previously inaccessible locations or irregularly shaped parts or cavities of a body such as the kidneys (FIG. 25).

[0044] Thus it is seen that based upon the forgoing description of the invention a flexible endoscope is disclosed comprising a first segment having a proximal end and a distal end thereof. The first segment is symmetric about an axis. A second segment comprising a flexible and interconnected linkage system is pivotably coupled to the first segment and, when subject to a force, is configurable along an arc having a variable radius of curvature.

[0045] It should be understood that any reference to first, second, front, rear, etc. or any other phrase indicating the relative position of one element or device with respect to another is for the purposes of explanation of the invention and, unless other wise noted, is not to be construed as limiting the invention. Furthermore, while preferred embodiments have been shown and described, various modifications may be made thereto without departing from the true spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustration and not limitation. 

What is claimed is:
 1. An endoscope comprising: a first segment having a proximal end and a distal end thereof wherein the first segment is symmetric about an axis; and a second segment comprising a flexible and interconnected linkage system, pivotably coupled to the first segment and when subject to an applied force, configurable along an arc extending from the axis and having a variable radius of curvature.
 2. The endoscope as set forth in claim 1 wherein the linkage system comprises: a first set of interconnected pivotable vertebrae extending from the distal end of the first segment; wherein each of the pivotable vertebrae comprises a body having: a front face beveled at a first and second angle; a rear face beveled at a third and fourth angle; a first pivot member projecting from the front face; and a second pivot member projecting from the rear face; wherein the first pivot member of one vertebrae is pivotably coupled about a rotational axis to the second pivot member of a second vertebrae.
 3. The endoscope as set forth in claim 2 further comprising a set of guide wires for applying a force to the endoscope.
 4. The endoscope as set forth in claim 3 further comprising means for guiding the set of guide wires along the endoscope.
 5. The endoscope as set forth in claim 4 wherein means for guiding the set of guide wires comprises means for guiding the set of guide wires within the body.
 6. The endoscope as set forth in claim 1 wherein the arc subtends an angle of from zeros degrees to greater than 180 degrees.
 7. The endoscope as set forth in claim 3 wherein the set of guide wires are attached to a vertebrae at variable distances from an axis of the body.
 8. The endoscope as set forth in claim 7 wherein variable moments are developed in the body when the set of guide wires is subject to a force.
 9. The endoscope as set forth in claim 2 wherein the front and rear face are beveled at about seven degrees.
 10. The endoscope as set forth in claim 2 wherein the body is generally cylindrical.
 11. A flexible endoscope comprising: a pivotably interconnected set of links configurable along an arc having a variable radius of curvature; a set of guide wires connected to the set of links for applying force to the set of links; wherein a first vertebrae is subject to a first torque and a second vertebrae is subject to a second torque different than the first torque.
 12. The endoscope as set forth in claim 11 wherein each of the pivotable links comprises a body having: a front face beveled at a first and second angle; a rear face beveled at a third and fourth angle; a first pivot member projecting from the front face; and a second pivot member projecting from the rear face; wherein the first pivot member of one vertebrae is pivotably coupled about a rotational axis to the second pivot member of a second vertebrae.
 13. The endoscope as set forth in claim 12 further comprising a set of guide wires for applying a force to the endoscope.
 14. The endoscope as set forth in claim 12 further comprising means for guiding the set of guide wires along the endoscope.
 15. The endoscope as set forth in claim 13 wherein means for guiding the set of guide wires comprises means for guiding the set of guide wires within the body.
 16. The endoscope as set forth in claim 11 wherein the arc subtends an angle of from zeros degrees to greater than 180 degrees.
 17. The endoscope as set forth in claim 12 wherein the set of guide wires is attached to a vertebrae at variable distances from an axis of the body.
 18. The endoscope as set forth in claim 17 wherein variable moments are developed in the body when the set of guide wires is subject to a force.
 19. The endoscope as set forth in claim 12 wherein the front and rear face are beveled at about seven degrees.
 20. The endoscope as set forth in claim 12 wherein the body is generally cylindrical.
 22. The endoscope as set forth in claim 11 wherein the radius of curvature is calculated according to the following equation: $R_{i} = \frac{V_{L}}{2\quad {\sin \left( \frac{\sum\Omega}{2{\sum V}} \right)}}$

wherein i=1, 2, V_(L) is the length of the vertebrae, Ω is the bend angle between adjacent vertebrae, ΣΩ is the total bend angle, ΣV is the total number of vertebrae links.
 23. The endoscope as set forth in claim 1 wherein the radius of curvature is calculated according to the following equation: $R_{i} = \frac{V_{L}}{2\quad {\sin \left( \frac{\sum\Omega}{2{\sum V}} \right)}}$

wherein i=1, 2, V_(L) is the length of the vertebrae, Ω is the bend angle between adjacent vertebrae, ΣΩ is the total bend angle, ΣV is the total number of vertebrae links.
 24. The endoscope as set forth in claim 1 wherein the radius of curvature increases along the arc.
 25. The endoscope as set forth in claim 1 wherein the radius of curvature decreases along the arc.
 26. The endoscope as set forth in claim 1 wherein the variable radius of curvature comprises two or more radii of curvature.
 27. The endoscope as set forth in claim 1 wherein the variable radius of curvature comprises a first radius of curvature when the second segment is configured in a first direction and a second radius of curvature when the second segment is configured in a second direction.
 28. The endoscope as set forth in claim 11 wherein the radius of curvature increases along the arc.
 29. The endoscope as set forth in claim 11 wherein the radius of curvature decreases along the arc.
 30. The endoscope as set forth in claim 11 wherein the variable radius of curvature comprises two or more radii of curvature.
 31. The endoscope as set forth in claim 11 wherein the variable radius of curvature comprises a first radius of curvature when the second segment is configured in a first direction and a second radius of curvature when the second segment is configured in a second direction.
 32. An endoscope comprising: a first segment having a proximal end and a distal end thereof wherein the first segment is symmetric about an axis; and a second segment comprising a flexible and interconnected linkage system, pivotably coupled to the first segment and configurable along an arc having a variable angle of articulation.
 33. The endoscope as set forth in claim 32 wherein the arc subtends a first angle of articulation when configured in a first direction and a second angle of articulation when configured in a second direction.
 34. The endoscope as set forth in claim 33 wherein the first angle of articulation is about 180 degrees.
 35. The endoscope as set forth in claim 33 wherein the second angle of articulation is greater than 180 degrees.
 36. The endoscope as set forth in claim 32 wherein the linkage system comprises: a first set of interconnected pivotable vertebrae extending from the distal end of the first segment; wherein each of the pivotable vertebrae comprises a body having: a front face beveled at a first and second angle; a rear face beveled at a third and fourth angle; a first pivot member projecting from the front face; and a second pivot member projecting from the rear face; wherein the first pivot member of one vertebrae is pivotably coupled about a rotational axis to the second pivot member of a second vertebrae.
 37. The endoscope as set forth in claim 32 wherein the arc comprises a variable radius of curvature.
 38. The endoscope as set forth in claim 37 wherein the radius of curvature changes as the angle of articulation changes.
 39. An endoscope comprising: a first segment having a proximal end and a distal end thereof wherein the first segment is symmetric about an axis; and a second segment comprising a set of variable length pivotably interconnected links, pivotably coupled to the first segment.
 40. The endoscope as set forth in claim 39 wherein the set of variable length links comprises: a first group of links pivotably coupled to the second segment and having a first length; and a second group of links pivotably coupled to the first group and having a second length different from the first length.
 41. The endoscope as set forth in claim 40 wherein the first and second group of links comprises: a set of pivotably interconnected vertebrae extending from the distal end of the first segment; wherein each of the pivotably interconnected vertebrae comprises a body having: a front face beveled at a first and second angle; a rear face beveled at a third and fourth angle; a first pivot member projecting from the front face; and a second pivot member projecting from the rear face; wherein the first pivot member of one vertebrae is pivotably coupled about a rotational axis to the second pivot member of a second vertebrae.
 42. The endoscope as set forth in claim 1 wherein the arc lies in a plane.
 43. The endoscope as set forth in claim 42 wherein the arc is a spiral.
 44. The endoscope as set forth in claim 1 wherein the arc lies on a geometrical body.
 45. The endoscope as set forth in claim 44 wherein the geometrical body is a cone.
 46. The endoscope as set forth in claim 43 wherein the spiral has an increasing radius of curvature.
 47. The endoscope as set forth in claim 43 wherein the spiral has a decreasing radius of curvature.
 48. The endoscope as set forth in claim 37 wherein the radius of curvature increases along the arc.
 49. The endoscope as set forth in claim 37 wherein the radius of curvature decreases along the arc.
 50. The endoscope as set forth in claim 3 wherein the set of guide wires is circumferentially positioned at varying rotational angles about an axis of the body.
 51. The endoscope as set forth in claim 13 wherein the set of guide wires is circumferentially positioned at varying rotational angles about an axis of the body.
 52. The endoscope as set forth in claim 36 further comprising a set of guide wires for applying a force to the endoscope.
 53. The endoscope as set forth in claim 52 wherein the set of guide wires is circumferentially positioned at varying rotational angles about an axis of the body.
 54. The endoscope as set forth in claim 52 wherein the set of guide wires is attached to a vertebrae at variable distances from an axis of the body.
 55. The endoscope as set forth in claim 41 further comprising a set of guide wires for applying a force to the endoscope.
 56. The endoscope as set forth in claim 55 wherein the set of guide wires is circumferentially positioned at varying rotational angles about an axis of the body.
 57. The endoscope as set forth in claim 55 wherein the set of guide wires is attached to a vertebrae at variable distances from an axis of the body. 